The discovery and impact of quantum Hall effect and other phenomena of topological nature in condensed matter physics has spurred the extension of these ideas to photonics [1]}, [2]}, resulting in the emergence of topological photonics [3]}, [4]}, [5]}, [6]}. As part of these developments in topological photonics, new phenomena and applications, such as unidirectional, topologically protected light propagation in which disorder-induced backscattering is suppressed [1]}, have been demonstrated and reviewed [2]}, [3]}, [4]}, [5]}, [6]}. By analogy with the time-reversal symmetry breaking feature of quantum Hall effect, which induces gapless edge states [13]}, [14]}, early research efforts have focused on the generation of topologically-protected edge states in magneto-optical photonic crystals (PhCs) under an external magnetic field [15]}, [16]}, [17]}, [18]}. However, magneto-optic photonic crystals only have strong response to an applied magnetic field at microwave frequencies, so that extending these phenomena to the optical domain required alternative solutions. To this end, in time-reversal invariant photonic systems, phenomena analog to quantum spin-Hall [19]}, [20]}, [21]}, [22]} and quantum valley-Hall [23]}, [24]}, [25]}, [26]} effects have been demonstrated upon breaking the spin-conservation and spatial-inversion symmetries, respectively. Topologically-protected edge modes have been explored not only in the context of fundamental science, but also with the aim to fulfil their potential for new device applications, such as robust light-transmission devices [27]}, [28]}, optical signal processing devices [29]}, time-delay lines [30]}, [31]}, dispersion-engineering devices [32]}, and sensors [33]}.
